3.2.1.1 First

Le premier modele applique un modele glm1 qui utilise la fonction de lien binomiale et la variable “id” comme effet aléatoire pour prendre en compte le fait que les observations sont repetees sur les mêmes individus sur plusieurs annees.

glm1 <- glmer(fec ~ age + (1| id),data=cham2, family = binomial)
summary(glm1)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1212.3   1226.7   -603.2   1206.3      906 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9150 -1.0621  0.6421  0.7819  1.1219 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.3319   0.5761  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.83210    0.20527   4.054 5.04e-05 ***
## age         -0.04723    0.01946  -2.426   0.0152 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##     (Intr)
## age -0.905

Anova(glm1)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##      Chisq Df Pr(>Chisq)  
## age 5.8874  1    0.01525 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

surdispersion_glm1 <- 1212/906;surdispersion_glm1

## [1] 1.337748

Interpretation des coefficients:

summary(glm1)$coefficients

##                Estimate Std. Error   z value     Pr(>|z|)
## (Intercept)  0.83209798  0.2052743  4.053590 5.043751e-05
## age         -0.04722673  0.0194638 -2.426388 1.524995e-02

exp(summary(glm1)$coefficients[2])

## [1] 0.9538711

Coeff <- ((1/exp(summary(glm1)$coefficients[2]))-1)*100

Avec le modele glm1, AIC/df = 1.3 donc il n’y a pas de surdispersion observee. Il est 4.8359681% moins vraisemblable que les chamois aient un petit lorsque leur age augmente d’un an (p-value = 0.0152).

3.2.1.2 Second

On ajoute la variable “year” en effet additif ou multiplicatif car il pourrait y avoir un effet “annee” dans la tendance observee sur la fecondite annuelle.

glm2 <- glmer(fec ~ age+ year + (1| id),data=cham2, family = binomial)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.166371 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

La variable “year” doit être centree normee pour pouvoir faire converger le modele.

year_scale<-scale(cham2$year, center=TRUE, scale= TRUE)
glm2 <- glmer(fec ~ age+ year_scale + (1| id),data=cham2, family = binomial)
summary(glm2)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + year_scale + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1212.4   1231.7   -602.2   1204.4      905 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0424 -1.0533  0.6394  0.7823  1.1856 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.327    0.5719  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.75566    0.21150   3.573 0.000353 ***
## age         -0.03888    0.02023  -1.922 0.054627 .  
## year_scale  -0.11728    0.08562  -1.370 0.170774    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) age   
## age        -0.911       
## year_scale  0.253 -0.291

glm3 <- glmer(fec ~ age*year_scale + (1| id),data=cham2, family = binomial)
summary(glm3)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age * year_scale + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1212.3   1236.4   -601.2   1202.3      904 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9099 -1.0508  0.6212  0.7703  1.2340 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.398    0.6309  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     0.78482    0.21836   3.594 0.000325 ***
## age            -0.04011    0.02080  -1.929 0.053787 .  
## year_scale      0.16827    0.21931   0.767 0.442931    
## age:year_scale -0.02916    0.02058  -1.417 0.156513    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age    yr_scl
## age         -0.909              
## year_scale   0.202 -0.171       
## age:yer_scl -0.100  0.048 -0.916

On n’observe pas de surdispersion pour les deux modeles testes. Que ce soit en effet mutiplicatif ou additif, la variable “year” n’a pas un effet significatif en addition à la variable “age” (p value > 0.1 en effet additif et multiplicatif). La variable “age” a un effet plus marque que la variable “year” avec une p value proche de 0.5.

3.2.1.3 Third

Test du modele avec deux effets aleatoires (variables “id” et “year”)

glm4<- glmer(fec ~ age + (1| id) + (1| year),data=cham2, family = binomial)
summary(glm4)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + (1 | id) + (1 | year)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1212.2   1231.5   -602.1   1204.2      905 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0185 -1.0136  0.6258  0.7816  1.2299 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.34280  0.5855  
##  year   (Intercept) 0.07463  0.2732  
## Number of obs: 909, groups:  id, 163; year, 26
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.82199    0.21943   3.746  0.00018 ***
## age         -0.04585    0.01985  -2.310  0.02089 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##     (Intr)
## age -0.867

Anova(glm4)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##      Chisq Df Pr(>Chisq)  
## age 5.3362  1    0.02089 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

surdispersion_glm4 <- 1212/905;surdispersion_glm4

## [1] 1.339227

Les resultats du modele glm4 sont similaires à ceux du modele glm1 (AIC, df, p value et coefficients similaires) donc le fait d’ajouter la variable “year” comme effets aléatoires n’apportent pas plus d’explication sur la variance observee.

4.2.1.1 First

Le premier modele applique un modele glm5 qui utilise la fonction de lien binomiale et la variable “id” comme effet aléatoire pour prendre en compte le fait que les observations sont repetees sur les mêmes individus sur plusieurs annees.

glm5 <- glmer(fec ~ year_scale + (1| id),data=cham2, family = binomial)
summary(glm5)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year_scale + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1214.1   1228.6   -604.1   1208.1      906 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8977 -1.0434  0.6474  0.7799  1.1928 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.3358   0.5794  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.38601    0.08734    4.42 9.89e-06 ***
## year_scale  -0.16692    0.08263   -2.02   0.0434 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr)
## year_scale -0.028

Anova(glm5)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##             Chisq Df Pr(>Chisq)  
## year_scale 4.0807  1    0.04337 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

surdispersion_glm5 <- 1214/906;surdispersion_glm5

## [1] 1.339956

Pas de surdispersion observee. D’apres la p-value<0.05, il y a aurait un effet significatif de la variable “year” sur la fecondite annuelle. Or, graphiquement, l’effet de la variable “year” semble negligeable. On se rend compte que l’age moyen de la population augmente avec les annees et on sait grace au modele glm1 que la variable “age” a un effet significatif sur la fecondite annuelle. Ainsi, il est important de regarder le modele glm3 qui presente les effets multiplicatids “year” et “age”.

glm3 <- glmer(fec ~ age*year_scale + (1| id),data=cham2, family = binomial)
summary(glm3)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age * year_scale + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1212.3   1236.4   -601.2   1202.3      904 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9099 -1.0508  0.6212  0.7703  1.2340 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.398    0.6309  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     0.78482    0.21836   3.594 0.000325 ***
## age            -0.04011    0.02080  -1.929 0.053787 .  
## year_scale      0.16827    0.21931   0.767 0.442931    
## age:year_scale -0.02916    0.02058  -1.417 0.156513    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age    yr_scl
## age         -0.909              
## year_scale   0.202 -0.171       
## age:yer_scl -0.100  0.048 -0.916

La variable “age” a un effet avec une p value proche de 0.5 alors que les p value associees à la variable “year” et aux effets multiplicatifs ne sont pas significatifs (p valu>0.1). La variable “year” n’a donc pas d’effet significatif sur la fecondite annuelle des chamois.

5.2.1.1 First => Voir avec Karim pour questions. Pas l’impression de pouvoir deduire de relation quand prise en compte du nombre d’annees de suivi dans la relation

test1 <- lm(feconditetotale~long, data = cham_id)
summary(test1)

## 
## Call:
## lm(formula = feconditetotale ~ long, data = cham_id)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2395 -1.6491 -0.3901  1.7214  8.5738 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.28163    0.63538   0.443    0.658    
## long         0.25904    0.05098   5.081 1.03e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.66 on 161 degrees of freedom
## Multiple R-squared:  0.1382, Adjusted R-squared:  0.1328 
## F-statistic: 25.81 on 1 and 161 DF,  p-value: 1.031e-06

plot(test1)

hist(resid(test1))

#Non homogeneite des residus

test2 <- lm(feconditetotale~log(long), data = cham_id)
summary(test2)

## 
## Call:
## lm(formula = feconditetotale ~ log(long), data = cham_id)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.3236 -1.8056 -0.3497  1.7138  8.6503 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -3.0910     1.2331  -2.507   0.0132 *  
## log(long)     2.6837     0.5079   5.283 4.07e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.645 on 161 degrees of freedom
## Multiple R-squared:  0.1478, Adjusted R-squared:  0.1425 
## F-statistic: 27.91 on 1 and 161 DF,  p-value: 4.066e-07

plot(test2)

#Non homogeneite des residus

test3 <- lm(sqrt(feconditetotale)~long, data = cham_id)
summary(test3)

## 
## Call:
## lm(formula = sqrt(feconditetotale) ~ long, data = cham_id)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.33973 -0.44205  0.02458  0.62207  1.71466 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.86498    0.19205   4.504 1.28e-05 ***
## long         0.06412    0.01541   4.161 5.15e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8041 on 161 degrees of freedom
## Multiple R-squared:  0.09708,    Adjusted R-squared:  0.09148 
## F-statistic: 17.31 on 1 and 161 DF,  p-value: 5.151e-05

plot(test3)

#Non homogeneite des residus

cham_id2 <- cham_id[cham_id$feconditetotale!=0,]
test4 <- lm(log(feconditetotale)~(log(long)), data = cham_id2)
summary(test4)

## 
## Call:
## lm(formula = log(feconditetotale) ~ (log(long)), data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.46036 -0.48276  0.06982  0.58994  1.20898 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.1012     0.3569  -3.086  0.00243 ** 
## log(long)     0.8863     0.1468   6.039 1.24e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6879 on 145 degrees of freedom
## Multiple R-squared:  0.201,  Adjusted R-squared:  0.1955 
## F-statistic: 36.47 on 1 and 145 DF,  p-value: 1.24e-08

plot(test4)

#Non homogeneite des residus

test5 <- lm(log(feconditetotale+1)~(long), data = cham_id2)
summary(test5)

## 
## Call:
## lm(formula = log(feconditetotale + 1) ~ (long), data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09484 -0.34652 -0.01657  0.41983  0.97945 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.63262    0.13315   4.751 4.82e-06 ***
## long         0.06419    0.01075   5.971 1.74e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5007 on 145 degrees of freedom
## Multiple R-squared:  0.1974, Adjusted R-squared:  0.1918 
## F-statistic: 35.65 on 1 and 145 DF,  p-value: 1.736e-08

plot(test5)

#Non homogeneite des residus

test6 <- lm(fectotrelative~long, data = cham_id)
summary(test6)

## 
## Call:
## lm(formula = fectotrelative ~ long, data = cham_id)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57107 -0.22551  0.01043  0.21283  0.44332 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.5545229  0.0694994   7.979 2.61e-13 ***
## long        0.0007195  0.0055768   0.129    0.898    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.291 on 161 degrees of freedom
## Multiple R-squared:  0.0001034,  Adjusted R-squared:  -0.006107 
## F-statistic: 0.01664 on 1 and 161 DF,  p-value: 0.8975

plot(test6)

#Non homogeneite des residus

test7 <- lm(log(fectotrelative)~long, data = cham_id2)
summary(test7)

## 
## Call:
## lm(formula = log(fectotrelative) ~ long, data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.51798 -0.28228  0.07845  0.31246  0.59766 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.613173   0.113211  -5.416 2.47e-07 ***
## long         0.005171   0.009140   0.566    0.572    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4257 on 145 degrees of freedom
## Multiple R-squared:  0.002203,   Adjusted R-squared:  -0.004678 
## F-statistic: 0.3201 on 1 and 145 DF,  p-value: 0.5724

plot(test7)

test8 <- glm(data=cham_id, feconditetotale~long, family="poisson")
summary(test8)

## 
## Call:
## glm(formula = feconditetotale ~ long, family = "poisson", data = cham_id)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.8849  -1.1120  -0.3623   0.8639   3.3159  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.24317    0.14334   1.697   0.0898 .  
## long         0.07730    0.01046   7.388 1.49e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 390.54  on 162  degrees of freedom
## Residual deviance: 335.96  on 161  degrees of freedom
## AIC: 772.39
## 
## Number of Fisher Scoring iterations: 5

test9 <- glm(data=cham_id, fectotrelative~long, family="quasipoisson")
summary(test9)

## 
## Call:
## glm(formula = fectotrelative ~ long, family = "quasipoisson", 
##     data = cham_id)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -1.06876  -0.32640   0.01389   0.26683   0.53371  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.589544   0.123663  -4.767 4.15e-06 ***
## long         0.001278   0.009907   0.129    0.898    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 0.1504962)
## 
##     Null deviance: 32.342  on 162  degrees of freedom
## Residual deviance: 32.340  on 161  degrees of freedom
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

6.2.1.1 First

glm11 <- glmer(fec ~ long + (1| id),data=cham2, family = binomial)
summary(glm11)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ long + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1218.0   1232.5   -606.0   1212.0      906 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7916 -1.0634  0.6517  0.7850  1.2047 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.3199   0.5656  
## Number of obs: 909, groups:  id, 163
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.23422    0.29351   0.798    0.425
## long         0.01175    0.02223   0.529    0.597
## 
## Correlation of Fixed Effects:
##      (Intr)
## long -0.956

Anova(glm11)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##       Chisq Df Pr(>Chisq)
## long 0.2793  1     0.5971

Pas de surdispersion. Pas d’effets significatifs observes de la variable “longevite” sur la fecondite annuelle (p value > 0.05)

6.2.1.2 Second => voir avec Karim la pertinence de segmenter en deux la variable

Graphiquement, une courbe concave se dessine donc on segmente la variable “longevite” en deux segments pour tester la relation longevite/fecondite annuelle sur les deux segments.

cham_long1 <- cham2[cham2$long<15,]
cham_long2 <- cham2[cham2$long>=15,]

plot16 <- ggplot(cham_long1, aes(x=long, y=fec)) +
    geom_count() + 
    labs(title = "Fécondité en fonction de la longevite",x="Longevite", y="Fécondité")+
    geom_smooth()+
    theme(plot.title = element_text(hjust = 0.5)); plot16

## Warning: Removed 408 rows containing non-finite values (`stat_sum()`).

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

## Warning: Removed 408 rows containing non-finite values (`stat_smooth()`).

glm12 <- glmer(fec ~ long + (1| id),data=cham_long1, family = binomial)
summary(glm12)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ long + (1 | id)
##    Data: cham_long1
## 
##      AIC      BIC   logLik deviance df.resid 
##    789.0    802.2   -391.5    783.0      585 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6864 -1.0755  0.6737  0.8230  1.1503 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.1568   0.3959  
## Number of obs: 588, groups:  id, 120
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept) -0.66433    0.39918  -1.664  0.09606 . 
## long         0.09835    0.03665   2.684  0.00728 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##      (Intr)
## long -0.971

Anova(glm12)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##       Chisq Df Pr(>Chisq)   
## long 7.2017  1   0.007283 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot17 <- ggplot(cham_long2, aes(x=long, y=fec)) +
    geom_count() + 
    labs(title = "Fécondité en fonction de la longevite",x="Longevite", y="Fécondité")+
    geom_smooth()+
    theme(plot.title = element_text(hjust = 0.5)); plot17

## Warning: Removed 408 rows containing non-finite values (`stat_sum()`).

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

## Warning: Removed 408 rows containing non-finite values (`stat_smooth()`).

glm13 <- glmer(fec ~ long + (1| id),data=cham_long2, family = binomial)
summary(glm13)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ long + (1 | id)
##    Data: cham_long2
## 
##      AIC      BIC   logLik deviance df.resid 
##    418.9    430.3   -206.5    412.9      318 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9648 -1.0836  0.5871  0.7880  1.2014 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.3949   0.6284  
## Number of obs: 321, groups:  id, 43
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  4.35885    1.43312   3.041  0.00235 **
## long        -0.23441    0.08423  -2.783  0.00539 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##      (Intr)
## long -0.994

Anova(glm13)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##       Chisq Df Pr(>Chisq)   
## long 7.7448  1   0.005387 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

7.2.1.1 First

lm14 <- lm(feconditetotale ~ pds,data=cham_pds)
summary(lm14)

## 
## Call:
## lm(formula = feconditetotale ~ pds, data = cham_pds)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4002 -2.1519 -0.6555  1.4273  9.5998 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  20.7763    23.0128   0.903    0.374
## pds          -0.8274     1.0838  -0.763    0.451
## 
## Residual standard error: 3.059 on 31 degrees of freedom
## Multiple R-squared:  0.01845,    Adjusted R-squared:  -0.01321 
## F-statistic: 0.5828 on 1 and 31 DF,  p-value: 0.451

lm15 <- lm(long ~ pds,data=cham_pds)
summary(lm15)

## 
## Call:
## lm(formula = long ~ pds, data = cham_pds)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.2055 -2.7518 -0.6201  1.9458  8.7945 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  -49.209     27.773  -1.772   0.0863 .
## pds            2.829      1.308   2.163   0.0384 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.692 on 31 degrees of freedom
## Multiple R-squared:  0.1311, Adjusted R-squared:  0.1031 
## F-statistic: 4.679 on 1 and 31 DF,  p-value: 0.03837

Impact de la longevite significatif sur le poids mais pas de la fecondite totale.